Question

Givenf(x) = x^2 + 12x + 27.What function shows function fwritten in vertex form?

Answer 1

EXPLANATION

Given the function f(x) = x^2 + 12x + 27

The expression in vertex form is as follows:

`f(x)=a(x-h)^2+k`

where a is the leading coefficient --> a=1

We need to compute h and k wich are the coordinates of the vertex (h,k)

The coordinates of the vertex are given by the following expression:

`x_{\text{vertex}}=(-b)/(2a)`

where b=12:

`x_v=(-12)/(2)=-6`

As x_v=-6 the expression of the function in standard form would be:

`f(x)=(x-(-6))^2+k`

Removing the parentheses:

`f(x)=(x+6)^2+k`

The only option that display this vertex form is the second one, hence that is the solution:

`f(x)=(x-6)^2-9`